(2x-9)(x+9)=x

Solution for (2x-9)(x+9)=x equation:

(2x-9)(x+9)=x

We move all terms to the left:

(2x-9)(x+9)-(x)=0

We add all the numbers together, and all the variables

-1x+(2x-9)(x+9)=0

We multiply parentheses ..

(+2x^2+18x-9x-81)-1x=0

We get rid of parentheses

2x^2+18x-9x-1x-81=0

We add all the numbers together, and all the variables

2x^2+8x-81=0

a = 2; b = 8; c = -81;
Δ = b2-4ac
Δ = 82-4·2·(-81)
Δ = 712
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{178}}{2*2}=\frac{-8-2\sqrt{178}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{178}}{2*2}=\frac{-8+2\sqrt{178}}{4}
$